Text-conditioned motion generators produce trackable whole-body motion, but they have no notion of scene-dependent safety: the same action may target an object or a person. Existing safeguards either inspect the prompt, require labeled motion data, or enforce geometric constraints; therefore, they do not directly account for how scene context changes a motion's meaning. We introduce contextual safety filtering (CSF), a training-free filter that grounds natural-language safety rules in safe and unsafe reference trajectories produced by the generator. For each active rule, safe and unsafe reference trajectories define an affine safety value that a safe reference tracking CBF-QP enforces. Across four pretrained generators with different architectures, CSF activates the intended rules in all explicit and scene-triggered unsafe cases and reduces the danger-event rate by up to 90%, while preserving 88-100% of benign motions. We demonstrate the complete system on a real-world Unitree G1, where it successfully prevents unsafe motions in a variety of scenarios, including interactions with humans and objects.